几道数学题，求教是否有更快的做法

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

(1)     2 is not a factor of n.

(2)     3 is not a factor of n. 

(C)   这题我一开始错了，后来看着答案后分析了很久才有点知道，考试时肯定不能这么分析

A.     5

B.     6

C.     9

D.     24

E.      36

(A)   这题我是把可能写了下来，是否排列这种方法可解

How many seconds will it take for a car that is traveling at a constant rate of 45 miles per hour to travel a distance of 22 yards?    (1 mile = 1,160 yards)

(C) 按理说这题很简单，可我死也没算出来选项里的答案，求教，别笑话我，O(∩_∩)O哈哈~

最後一題題目錯了~~是1760yrs

(1)     2 is not a factor of n.

(2)     3 is not a factor of n. 

(C)   这题我一开始错了，后来看着答案后分析了很久才有点知道，考试时肯定不能这么分析

我的做法是如下(不知道简单否)

1. (N-1)(N+1) =N^2-1

(1) 2 is not a factor  -  n is odd. (n-1)(n+1)=even * even - couldn't get the r since many results

(2) 3 is not a factor - possible prime n is 2, 5,7, hard to tell reminder when divided by 24

(1) + (2), not a factor of 6. then can be 5 or 7. 5-1=4 and 7-1 =6. then r=0

(1)&(2)       (n-1)(n+1)=2a*(2a+2) =4a(a+1)     8是其约数

                    (n-1)(n+1)=3b*(3b+2)                    

               Or (n-1)(n+1)=3b*(3b-2)                     这两种情况下 3是其约数

         So， 3和8一定是(n-1)(n+1)的约数，(n-1)(n+1)一定能被24整除

         So，
                            r=0

我又想了想，受scorpio2rd的启发，谢谢